Lake Eyre

Google Lake Eyre Yacht Club...

But I think the answer's "no" - not even in Hartigan Bay.

I cant help re the water but can suggest a camp or two. Lovely
bush camping in Parachilna Gorge (free), about 15k east of the
Prairie Hotel. A few charges at the pub first, let the missus drive out there & you will be set for a goodnight. You might like to consider Overland Corner for the night before. You can bush camp at Heron Bend (free) & its just a short drive across the floodplain to the OC pub, fabulous old place with heaps of history.
If you are going up the Ood track, we found Algebukkina Bridge
very acceptable for an overnighter, sorry, no pub, about 50k
south of Ood....have a great trip....oldbaz.

Re camping options: Excellent camping spot and interesting ruins at Farina about 50k before Maree or camp at Muloorina Station ($2/night) about 50k N/W of Maree (beautiful oasis with heaps of bird life)and access Lake at Level post bay another 45k away

No water in Lake eyre.
There has to be a heap in the lake before it is seen at the common viewing points at Level Post Bay and Halligans Bay. I've never seen water in Lake Eyre South from the Oodnadatta track.

Camping after the Flinders:
Farina (20k N of Lyndhurst) is a $3.50/head/night camp spot provided by the station owner. Can heat up the donkey for a hot shower, and its got good clean flushing loos. Have a look around the cemetary and ruins while you're there.

If you're visiting lake Eyre North, Muloorina Station has a similar camp area to Farina - nice shade, good spot and fees are donated to RFDS.

Coward Springs is privately run, and is a good spot, where you can have a hot dip.

William Creek has a great pub.Camping is out the back of the pub - a night there is usually a memorable experience.

Can turn left to go via Coober pedy if you want, or north to Oodnadatta.Algebuckina Bridge is south of Oodnadatta and on the Neales River, which usually has water.

If it were me, I'd stay away from the bitumen and continue north - a few options - call into Dalhousie and Mt Dare and take the Old Andado Track to Alice Springs, or continue north at Hamilton Station to Eringa waterhole, and take the Finke track or hit the bitumen at Kulgera.